Data modulation based on nonlinear dynamics

There are several optical encryption methods proposed and demonstrated which utilize chaos related modulations: chaos shift keying, chaos masking, chaos modulation, and so on.

Figure 2.1 Schematic diagram of chaos shift keying [54].

Chaos shift keying is implemented by encoding the data through direct current modulation of the transmitter, as shown in Figure 2.1. I0 and I1 are injection current

corresponding to data “0” and “1” respectively. C0 and C1 are chaos pattern generated

from I0 and I1 respectively. The basic idea of the scheme is modulating the data with

different chaos patterns. The receiver consists of two lasers driven by the selected parameters corresponding to transmitter’s “0” and “1” value (I0 and I1) independently.

Decoding of the data is done by subtracting the output of the receiver from the signal received. In this situation, true chaos synchronization is infeasible since the transmitter is current-modulated with the data while the receiver is not. The chaotic state of the transmitter is determined by the data.

Figure 2.2 Schematic diagram of chaos masking [55].

Transmitter LD Receiver LD Data(switching) I₀ I₁ C₀+ C₁ Receiver LD I₀ I₁

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₊

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The data modulation in chaos masking scheme is achieved by directly adding the data to the chaotic waveform, as shown in Figure 2.2. The demodulation operation is same as chaos shift keying, subtracting the output of the receiver from the received signal. In this case, the data is only injected to the receiver and is extracted from transmitted signal by subtracting a synchronized chaotic signal C’. However, it has not been mathematically proven whether the synchronized signal (C’) can be identically reproduced from the transmitted signal (C+M). As the result, the true synchronization is infeasible. Nevertheless, the chaotic state of the transmitter is not influenced by the data.

Figure 2.3 Schematic diagram of chaos modulation [56].

In the additive chaos modulation, the data is also added to the chaotic output of the transmitter. Meanwhile, the information about the data is sent both to the transmitter and the receiver so that the true synchronization is achievable. And the chaotic state of transmitter, as well as the complexity of chaos, is related with the data.

A general feature of communication based on optical chaos is that the recovered data is affected by the channel noise along with the synchronization error. Figure 2.4 shows the decoded waveform of the three different schemes. As we can see, data recovery is quite difficult to achieve in chaos shift keying scheme because the encoded signal has frequent desynchronized bursts. The performance is affected by the resynchronization time. According to the report [57, 58], resynchronization is hard to achieve when bit rate is over 10Gb/s. The performance gets better when the bit duration gets longer than the resynchronization time. In 2005, Argyris with his team demonstrated a chaos-based communication system on commercial fibre links [59] and the result is perfectly accordance with the theory analysis. The performance of the system is degraded significantly when the bit duration is approaching synchronization time. Transmitter LD

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τ

+

τ

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Figure 2.4 Decoded signals of chaos shift keying (CSK), chaos masking (CMS) and additive chaos modulation (ACM) [60].

In the case of chaos masking scheme, the synchronization error is mainly caused by the difference between the transmitter and the receiver. The influence of the data is weak comparing to the encoded signal, which is domiated by the chaos synchronization. The performance can be improved by deploying a low-pass filter to eliminate the interference from the chaos synchronization.

The performance of additive chaos modulation is greatly improved compared to the previous schemes since the true synchronization can be achieved. As the result, the synchronization noise is minimized, and the channel noise as well as the transmitter noise will be the main noise source. Since both the chaos shift keying scheme and the chaos masking scheme could not achieve true synchronization, the decoding waveforms are apparently noise like for a NRZ signal. In the example of the chaos shift keying scheme, it is quite easy to distinguish the two chaos patterns by observing the amplitude difference. Only the additive chaos modulation scheme which is truely synchronized can recover a good waveform. Still, the occurrence of the desynchronization bursts occurs will degrade the performance significantly, as the example shown in Figure 2.4.

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The system performances measured by BER of these schemes are compared in Figure 2.5. The importance of the true chaos synchronization is revealed.

Figure 2.5. Performance comparisons of chaos shift keying (CSK), chaos masking (CMS) and additive chaos modulation (ACM) [60].

As a candidate in the optical layer for secure communication, although the optical chaos schemes have the comparable performance to traditional systems, they are too sensitive to the dispersion, distortion, nonlinear signal processing and noise. Besides, for any chaotic communication systems, the synchronization between the transmitter and the receiver is critical. It requires a good symmetry between the transmitter and the receiver to maintain high quality synchronization. Despite of these obstacles which prevent the optical chaos from commercial utilization, chaos-based secure communication scheme do have their advantages over the traditional encryption schemes. Optical chaos based schemes can be performed over continuous number fields. Both the chaos signal and data signal can be continuous signal rather than discrete digitized data. The encoded signal is noise-like and spectrum spread, which makes it difficult to perform a matched detection. Although the speed of optical chaos based scheme is limited by the time of synchronization, the coding process can still be implemented in all optical domain with high-speed analog signals.

The optical chaos based secure communication systems do have their weakness. It’s possible to break a chaos based system without searching for the secret key, as long as the encoded signals show low-order statistical characteristics corresponding to the data transmitted. In particular, transmission of binary data is risky, since even for the high-dimensional nonlinear dynamics, the transmitted signal pattern may be considered to reveal some information related data [61]. If the type of nonlinear dynamics is known

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to the attacker, it is possible for him to use generalized synchronization to decode the data. In [62], an optical chaos based scheme on Chua’s circuit is compromised by using generalized synchronization. The data is leaked from the variations in the synchronization error. In [63], an attack approach is proposed to break the optical chaos based system by reconstruct the secret chaotic dynamics completely without any knowledge about the type of the nonlinear dynamic. In this scheme, the attacker is using time delay to reconstruct the nonlinear dynamics part by part.

In summary, the security of a communication system is not only related to the data confidentiality, the availability of the system is also need to be considered and more important it is the first issue we should guarantee. It is still a long way to go for the chaotic secure communication before we mastered the chaos synchronization in optical layer and make it more feasible for practical application. After all, the security issues are highly bound to the practical implementation, and need time to evolve to prevent the attacks from every aspect.